Algebra1 Misleading Graphs and Statistics

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Algebra1Algebra1

Misleading GraphsMisleading Graphsand Statisticsand Statistics

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Warm UpWarm Up

1) 2x - 3 < 7

2) 3 (t - 1) ≥ -15

Solve each inequality and graph the solutions.

3) 6 - n < 2n + 9

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Graphs can be used to influence what people believe. The way data is displayed can influence how the data is interpreted.

Misleading Graphs and StatisticsMisleading Graphs and Statistics

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Misleading Bar GraphsMisleading Bar Graphs

The graph shows the size of tomatoes on plants that were treated with different fertilizers.

A) Explain why the graph is misleading.

The scale on the vertical axis beginsat 80. This exaggerates the differencesbetween the sizes of the bars.

B) What might someone believe because of the graph?

Someone might believe that thetomato treated with fertilizer D ismuch larger than the other tomatoes. It is only 4 grams larger than the tomato treated with fertilizer B.

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Now you try!

1. Who might want to use the graph below? Explain.

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Misleading line GraphsMisleading line Graphs

The graph shows the average price of gasoline in the U.S. in September.


The intervals on the vertical axis arenot equal.

B) What might people be influenced to believe by the graph?

Someone might believe that the price of gasoline increased the most between 1995 and 1997. However, the change between 1995 and 1997 was only $0.14/gal while the change between 1999 and 2001 was $0.17/gal.

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Now you try!


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A circle graph compares each category of a data set to the

whole. When anycategory is not represented in the graph, it may appear that another

categoryrepresents a greater percentage

of the total than it should.

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Misleading Circle GraphsMisleading Circle Graphs

The graph shows what percent of the total votes were received by three candidates for student council president.


The sections of the graph do not add to 100%, so the votes for at least one of the candidates is not represented.


Someone might believe that Smith won the election.

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Now you try!


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Statistics can be misleading because of the way the data is

collected or the waythe results are reported. A

random sample is a good way to collect unbiased data.

In a random sample , all members of the group being surveyed have

an equalchance of being selected.

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A researcher surveys people leaving a basketball game about what they like to watch on TV. Explain why the following statement is misleading: “80% of

people like to watch sports on TV.”

The sample is biased because people who attend sporting events are more likely to watch sports on TV than people

who watch TV but do not attend sporting events.

Misleading StatisticsMisleading Statistics

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4) A researcher asks 4 people if they have seasonal allergies. Three people respond yes. Explain why the

following statement is misleading: “75% of people have seasonal allergies.”

Now you try!

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Assessment

1 )The graph shows the average salaries of employees at three companies.

a. Explain why the graph is misleading.b. What might someone believe because of the graph?c. Who might want to use this graph?

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2) The graph shows hotel occupancy in San Francisco over four years.


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3 )The graph shows the nutritional information for a granola bar .


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4) Three students were surveyed about their favorite teacher. Two students

answer Mr. Gregory, and one answers Mr. Blaine. Explain why the following

statement is misleading: “Mr. Gregory is the favorite teacher of a majority

of the students.”

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5) A researcher surveys people at a shopping mall about whether they favor enlarging

the size of the mall parking lot. Explain why the following statement is misleading:

“85% of the community is in favor of enlarging the parking lot.”

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Misleading Bar GraphsMisleading Bar Graphs

The graph shows the size of tomatoes on plants that were treated with different fertilizers.


The scale on the vertical axis beginsat 80. This exaggerates the differencesbetween the sizes of the bars.


Someone might believe that thetomato treated with fertilizer D ismuch larger than the other tomatoes. It is only 4 grams larger than the tomato treated with fertilizer B.

Let’s review

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Misleading line GraphsMisleading line Graphs

The graph shows the average price of gasoline in the U.S. in September.


The intervals on the vertical axis arenot equal.

B) What might people be influenced to believe by the graph?

Someone might believe that the price of gasoline increased the most between 1995 and 1997. However, the change between 1995 and 1997 was only $0.14/gal while the change between 1999 and 2001 was $0.17/gal.

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Misleading Circle GraphsMisleading Circle Graphs

The graph shows what percent of the total votes were received by three candidates for student council president.


The sections of the graph do not add to 100%, so the votes for at least one of the candidates is not represented.


Someone might believe that Smith won the election.

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A researcher surveys people leaving a basketball game about what they like to watch on TV. Explain why the following statement is misleading: “80% of

people like to watch sports on TV.”

The sample is biased because people who attend sporting events are more likely to watch sports on TV than people

who watch TV but do not attend sporting events.

Misleading StatisticsMisleading Statistics

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You did a great job You did a great job today!today!

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Algebra1 Misleading Graphs and Statistics